Finite Group Databasebeta

← C₃×C₇×D₅₅₇ #37552688

Subgroups — C₃×C₇×D₅₅₇ #37552688

Order 23394.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₅₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₅₅₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₅₅₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅₅₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	D₅₅₇	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
7	C₅₅₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₇	—	557	1	no	maximal, Hall
9	C₃×C₇	D₅₅₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₇	—	557	1	no	Hall
11	C₇	C₃×D₅₅₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	557	1	no	Hall
13	C₃	C₇×D₅₅₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	557	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₅₅₇
commutator, cosocle, hypocenter	C₅₅₇	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₅₅₇	C₂
LCS	G ▷ C₅₅₇
UCS	C₁ ◁ C₃×C₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₇×C₅₅₇	C₂	semidirect
2. C₇×D₅₅₇	C₃	direct (N × H)
3. C₇×C₅₅₇	C₂×C₃	semidirect
4. C₃×D₅₅₇	C₇	direct (N × H)
5. C₃×C₅₅₇	C₂×C₇	semidirect
6. D₅₅₇	C₃×C₇	direct (N × H)
7. C₅₅₇	C₂×C₃×C₇	semidirect
9. C₃×C₇	D₅₅₇	direct (N × H)
11. C₇	C₃×D₅₅₇	direct (N × H)
13. C₃	C₇×D₅₅₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₇×C₅₅₇	2
C₇×D₅₅₇	3
C₃×D₅₅₇	7
C₂×C₃×C₇	557